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%% canonicalGravity.tex
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%% Made by Alex Nelson
%% Login   <alex@tomato>
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%% Started on  Fri Jun  5 11:50:17 2009 Alex Nelson
%% Last update Sat Jan 16 11:15:15 2010 Alex Nelson
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\documentclass[10pt,draft]{article}
\usepackage{notebk}
\numberwithin{equation}{section}

\title{Notes on Canonical Gravity}
\date{June 5, 2009}
\begin{document}
\maketitle
\tableofcontents
\begin{abstract}
A review of the ADM Hamiltonian formalism for classical General
Relativity.
\end{abstract}
\bigbreak
Just a few remarks on notation. Latin indices $i,j,\ldots$ will
be for spatial components of four-tensors, Greek indices
$\alpha,\beta,\ldots$ will be for spacetime components of
four-tensors.

We will approach the subject of the Hamiltonian formulation of
general relativity (also known as canonical formulation of
gravity, canonical dynamics for general relatvity, canonical
gravity, among countless other names -- canonical here refers to
the use of Hamiltonian formalism as opposed to the Lagrangian
formalism) by the following process. %first reviewing the notion of hypersurfaces. 
%We will then apply this to the 
We will perform the decomposition of spacetime into space
plus time, or the ADM form of the metric. Given such a
decomposition, we look at how the Lagrangian gives way to the
Hamiltonian formalism. Then we review the constraints of General
Relativity, both the Hamiltonian and Momentum constraints.

\section{A Review of Hypersurfaces}
\input{hypersurface}
\section{ADM Form of the Metric}
\input{admMetric}
\section{Einstein Hilbert Action to Canonical Variables}
\input{lagrangian}
\section{Canonical Dynamics}
\input{canonicalAction}

\nocite{*}
\bibliographystyle{elements}\footnotesize
\bibliography{canonicalGravity}
\end{document}
